Elliptic fibrations associated with the Einstein spacetimes

Abstract

Given a conformally nonflat Einstein spacetime we define a fibration $P$ over it. The fibres of this fibration are elliptic curves (2-dimensional tori) or their degenerate counterparts. Their topology depends on the algebraic type of the Weyl tensor of the Einstein metric. The fibration $P$ is a double branched cover of the bundle of null direction over the spacetime and is equipped with six linearly independent 1-forms which satisfy certain relatively simple system of equations.

15 pages, Latex

References in corpus (2)

• Twistor Bundles, Einstein Equations and Real Structures
• On a certain formulation of the Einstein equations

Cited by in corpus (2)

• On a certain formulation of the Einstein equations
• Extension of bundles of null directions